Thermal expansion of aluminum disc

In summary: Thanks!In summary, the equation tells you how length changes with temperature, and the engineer is using this to calculate how much the diameter will expand. The thickness of the aluminum doesn't matter, because the expansion is the same in all directions.
  • #1
jklops686
40
0
I have an aluminum disc that is 15in in diameter and about 1in thick. I am going to put it in a 400°F oven and I need to know how much the diameter will expand.

One of the engineers I work with(i'm an intern) is using what I found to be the linear expansion equation (ΔL/Li=αΔT)...so Length change = Original length x alpha(coefficient) x delta T. He's using 15in as the original length. I don't see how this can be accurate because it's a disc that is pretty thick. The calculation comes out to .03. Does this mean .03 in all directions? How do we take the thickness into account? What if the disc was 1ft thick? Should I use volume expansion to be more accurate?

Thanks
 
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  • #2
Using the formula, you'll see that the change in length depends on the initial length as well as the change in temperature, so the disk won't change by 0.03 inches in every direction.

How would you go about using the coefficient of volume expansion for this problem?
 
  • #3
ΔL/Li=3αΔT Then something
 
  • #4
If the disk is not constrained, then it expands linearly in all directions by the same percentage. If you want to find the change in volume, then you use ΔV/Vi=3αΔT. Notice that the coefficient of volume expansion is equal to 3 times the coefficient of linear expansion.

Chet
 
  • #5
That makes sense. I was thinking that when i stared at it for a minuet today. Thanks
 
  • #6
But what if the disc is constrained, like 500lbs on top of it?
 
  • #7
jklops686 said:
But what if the disc is constrained, like 500lbs on top of it?

As long as the force is constant, it would have no bearing on the thermal expansion, and the expansion would still be the same in all directions. Therefore, the 500 lb would not be considered a constraint. The kind of constraint I am referring to is if the material is prevented from fully expanding in a certain direction (i.e., constraint on the deformation, not on the loading). For example, consider a case where the material is not allowed to extend in a certain direction (i.e., zero strain). Under these circumstances, if the material were heated, the stress in the constrained direction would have to increase. The best way to understand this is to examine the 3D tensorial version of Hooke's law, in which thermal expansion is included. The easiest version to work with is where the strains are expressed in terms of the stresses.

Chet
 
  • #8
jklops686 said:
That makes sense. I was thinking that when i stared at it for a minuet today. Thanks

Interval for a stately 17th Century dance. Some typos introduce a whole new atmosphere of sophistication to the hurly burly of Physics. I wish there were more like this. :smile:
 
  • #9
This is why I love physics forums.
 

1. What is thermal expansion?

Thermal expansion is the tendency of a material to expand or contract in response to changes in temperature. When a material is heated, its molecules vibrate faster and take up more space, causing the material to expand. Conversely, when a material is cooled, its molecules slow down and take up less space, causing the material to contract.

2. How does thermal expansion affect aluminum discs?

Aluminum discs, like all materials, expand when heated and contract when cooled. This means that as the temperature of an aluminum disc increases, its diameter will increase and as the temperature decreases, its diameter will decrease. This expansion and contraction can have practical implications in applications where precise measurements or tight tolerances are necessary.

3. What is the coefficient of thermal expansion for aluminum?

The coefficient of thermal expansion (CTE) is a measure of how much a material will expand or contract per unit length for each degree change in temperature. The CTE for aluminum is approximately 23.1 x 10^-6 m/mK, meaning that for every 1 degree Celsius increase in temperature, an aluminum disc will expand by 23.1 micrometers per meter of its initial length.

4. Can thermal expansion cause damage to aluminum discs?

In most cases, thermal expansion will not cause damage to aluminum discs. However, in extreme temperature changes, such as rapid heating or cooling, the expansion and contraction of the material can cause stress and potentially lead to cracking or warping. It is important to consider the expected temperature changes and the CTE of aluminum when designing and using aluminum discs in various applications.

5. How can thermal expansion of aluminum discs be controlled?

Thermal expansion of aluminum discs can be controlled by using materials with lower CTE values, such as certain alloys, or by incorporating design features to accommodate for the expected expansion and contraction. These design features can include gaps, slots, or other methods of allowing the material to expand and contract without causing damage. Additionally, using insulation or other methods to regulate the temperature around the aluminum disc can also help control its expansion and contraction.

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